# Problem 247: Squares under a hyperbola
Consider the region constrained by 1 ≤ x and 0 ≤ y ≤ 1/x. Let S1 be the
largest square that can fit under the curve. Let S2 be the largest
square that fits in the remaining area, and so on. Let the index of Sn
be the pair (left, below) indicating the number of squares to the left
of Sn and the number of squares below Sn. The diagram shows some such
squares labelled by number. S2 has one square to its left and none
below, so the index of S2 is (1,0). It can be seen that the index of S32
is (1,1) as is the index of S50. 50 is the largest n for which the index
of Sn is (1,1). What is the largest n for which the index of Sn is
(3,3)?